EAMCET Engineering 2009 Solved Paper

The displacement of particle, executing SHM
y=5sin‌(4t+‌

π

3

) . . . (i)
Velocity of particle
(‌

dy

dt

)‌=‌

5d

dt

sin‌(4t+‌

π

3

)
‌=5‌cos(4t+‌

π

3

)⋅4
‌=20‌cos(4t+‌

π

3

)
Velocity at t=(‌

T

4

)
(‌

dy

dt

)t=‌

T

4

=20‌cos(4×‌

T

4

+‌

π

3

)
or u=20‌cos(T+‌

π

3

) . . . (ii)
Comparing the given equation with standard equation of SHM, given by
y=asin‌(ωt+φ)
We get
ω=4
‌ As ‌‌ω=‌

2π

T

⇒T‌=‌

2π

ω

‌ or ‌‌T‌=‌

2π

4

‌ or ‌‌T‌=‌

π

2

)
Now, putting value of T in Eq. (ii), we get
u‌=20‌cos(‌

π

2

+‌

π

3

)
‌=−20sin‌‌

π

3

‌=−20×‌

√3

2

‌=−10×√3
The kinetic energy of particle,
KE‌=‌

1

2

mu2
m‌=2g=2×10−3‌kg
‌=‌

1

2

×2×10−3×(−10√3)2
‌=10−3×100×3
‌=3×10−1
KE=0.3J